The main topic of this thesis is the quasi-optical analysis of optical systems for experiments used to measure the polarisation anisotropies of the cosmic microwave background. The polarisation signal is so low and difficult to measure that very accurate modelling and a deep understanding and characterisation of the instruments used to make such measurements is essential. The two instruments investigated in this thesis are the Millimetre-Wave Bolometric Interferometer (MBI) and the Q and U Bolometric Interferometer for Cosmology (QUBIC), both of which are collaborations between institutes in Europe and the United States. A prototype of MBI called MBI-4 has already been built and has been used for experimental observations. The main aim of this prototype has been to prove the concept of bolometric interferometry for measurements of the CMB. In this thesis the optical combiner of MBI-4 is designed and modelled in detail, taking into account mechanical tolerances and truncations effects, amongst others. The QUBIC instrument is currently in the design stage, having evolved from both MBI-4 and BRAIN, an experiment located in Antarctica as a test for a more elaborate instrument. The optical design of QUBIC is also analysed, including a physical optics analysis of lenses, although not in the same detail as MBI-4. A number of techniques are used in this analysis, including Gaussian beam modes and physical optics, to allow for a complete model of the optical systems to be obtained. As part of this modelling, a mode-matching technique is applied to predict the beam patterns of horn antennas. In this thesis, the technique is extended to include a transition from rectangular to circular waveguide geometries as such a junction occurs in the MBI back-to-back horns. The results obtained in this thesis give a useful insight into the power and usefulness of various optical design and analysis techniques as well as criteria for the successful design of current and future interferometry experiments.